Badass Decay: Lustbader changes Bourne from an unstoppable juggernaut into a whining wimp who wouldn't win without outside help.
Creator's Pet: Lustbader's Arkadin in the books. Lustbader keeps filling the narration with Arkadin's past and making Bourne exhausted so Bourne cannot kill Arkadin. When someone writes Bourne novels and guarantees upfront that the villain is going to have his own trilogy, you know that villain is a pet.
Designated Hero: Arkadin, in the flashbacks of his past. The narration is meant to make readers sympathize with him, his tormented life in Nizhny Tagil, and his struggle against various Russian crime bosses. The problem is that, even considering all that, he is still a murderer, a terrorist, in a life of crime for selfish gains, and no better than any other Russian gangsters he kills.
Darkness-Induced Audience Apathy / Fanon Discontinuity: One of the problems with Legacy and Jason Bourne is that they undo the hard-won victory at the conclusion of Ultimatum, showing that the bad guys managed to prevent the incriminating documents from being made public and covered their tracks further by slandering and murdering even more people than they already had. In a world as drab, bleak and depressing as the Bourne movies already are, many fans simply choose to pretend that the latter two movies simply never happened in order to enjoy some ray of sunshine.
Cross and Shearing are extremely popular in fanfiction.
Popular Australian Actor/Comedian Shane Jacobson's brief appearance as the Factory Owner in Legacy was well received by Aussies, many of whom paid more attention to him in his scenes than anyone actually relevant to the plot.
The first two sequels kept getting more acclaim from critics, with the third film The Bourne Ultimatum generally being seen as the best.
Inverted with the later films. Though not technically a sequel, Legacy didn't receive the same amount of praise that the first three Damon films did, and despite bringing Damon back, neither has Jason Bourne.
Iron Woobie: Let's just say Bourne had a lot to go through.
Only the Creator Does It Right: One may argue that the Bourne series has two daddies with Doug Liman and Paul Greengrass. With The Bourne Identity, director Doug Liman gave the film a unique style, but it was Paul Greengrass who would flesh it out in its sequels The Bourne Supremacy and The Bourne Ultimatum, with Liman still involved as executive producer, garnering even greater acclaim. But when Greengrass turned down the offer to direct The Bourne Legacy, Matt Damon left with him, saying he wouldn't do any more movies without him, and Liman left too. This is part of why Legacy wasn't as well-received as its predecessors. It should be noted that Tony Gilroy wrote all four films (and directed Legacy). The fact that he wasn't involved with Jason Bourne even though Greengrass and Damon returned probably led to it also not being as well-received as the original trilogy.
A notable aversion that is somewhere between this and Even Better Sequel. Each one of the first three films is considered to be quite good and at the least on par with each other. Although there are a group of people who consider the third film the best due to having the highest HSQ.
Though some considered Supremacy to be a bit of a step down, with more of an action emphasis and an overload of Jitter Cam (thankfully toned down in Ultimatum).
Legacy is a bit more divisive in this respect, with its very existence of trying to make the series a franchise and reverting what should have wrapped up the series in Ultimatum. That said, the movie was much better received than comparable attempts due to having a few shared members of the production (the same writer, who also takes on director duties) and a great cast with Renner, Weisz and Norton.
Jason Bourne (the fifth movie) however seems to have fallen into that territory, mainly because of criticism regarding the lack of innovation storywise.
Song Association: Moby's "Extreme Ways", due to it being used as the credits song for each movie. The first trailer for Jason Bourne only needed the song's first two notesnote A violin triad held for a whole note, admittedly pretty iconic to signify that the movie it was advertising was a Bourne movie.